What sets the absolute value of players' Elo rating?

Question

I understand that the way the Elo updating process works, if player A has a 66% chance of beating player B, then A's Elo rating will converge to be 100 higher than B, and so forth for 74%, ... etc. Assume for the purposes of this question that the assumptions of the Elo rating system actually hold (e.g. if A has a 66% chance of beating B, and B has 66% chance of beating C, then A always has a 74% chance of beating C). However, this description is consistent with player and ELO of B having Elo of 10 million, and player A having an Elo of 10 million + 100.

EDIT: So there is an arbitrary "scaling" in the ELO rating: In a world with only two players, scores (1000, 1100) are equivalent in interpretation to (2000,2100). How does the algorithm that is used in the chess world end up setting this absolute scale?

• E.g. does it always try to make sure that the mean score is 1500, by adjusting everyone's score uniformly when the mean deviates? If so, who is included in the mean? (everyone who went to tournaments?)

• Or does it simply always assign a particular initial score?

(Note, this question looks similar, but doesn't actually answer my question).

Answer 1

There literally is no "absolute value" for Elo ratings, if I understand what you mean by that. A single player's Elo rating, in isolation, means nothing. The only thing the Elo rating scale is good for is comparing two (or more) players; the only thing that matters is the difference between the players' ratings. Two players' ratings could be 1500 and 1600, or 10,000,000 and 10,000,100 - the interpretation of the ratings is exactly the same either way. You mentioned that the Elo rating system was designed so that an average club player would have a rating of 1500 (I've actually never seen it described that way before - what I had previously seen was that it was designed so that a player who was capable of scoring 50% in the US Open would have a rating of 2000). But that is arbitrary; any number could have been picked.

The situation you describe where the billion terrible players come into the rating system, dump a bunch of points, and then leave, is an age-old issue that's called "ratings inflation" - this is not unusual, and in the aftermath of "The Queen's Gambit", I'm wondering if we're about due for a new period of ratings inflation very soon... There's an analogous "ratings deflation" scenario that happens when a bunch of players come into the system with low ratings, play very well, take a bunch of points from established players, and then leave the system. This happens in areas with strong scholastic chess programs, where it often happens that kids come into the system at low ratings, their level of ability increases much faster than the ability of the rating system to keep up with it, and then they leave the player population after they leave the scholastic chess program. So they have taken away rating points from established players, who have no hope of getting them back from those player, because those players have left the player population. There are a number of approaches one can take to combat this problem, probably the simplest (and the one I heard of the most in the early days of the Elo rating system in the USCF) was simply doing periodic manual adjustments to players' ratings to push them back into line to where you want the average rating to be - for example, something like declaring, "On date X, all players ratings will be manually increased (or decreased) by N points, across the board".

This is assuming you actually see ratings inflation / deflation as a "problem" of course, since as stated, the actual number is arbitrary. And it's really not a "problem" if you have no expectations of the rating system other than it being valid at some specific moment in time. The place you run into "problems" is trying to use ratings to compare players across large gaps of time - like, "Could Bob Smith, who was rated 2100 in the year 1989, have beaten Bill Jones, who is rated 2000 in the year 2021?" Ratings inflation / deflation completely messes up trying to use players ratings to discuss questions like that.

Answer 2

What sets the absolute value of players' ELO rating?

This is one of those "Why did you stop beating your wife?" questions. Your assumption is wrong. There is no "absolute value of players' ELO rating".

I read that the "the USCF initially aimed for an average club player to have a rating of 1500".

How does this happen exactly?

In the initial calculation this happens by a simple and easy mathematical process of fitting a normal curve to a dataset. I think you missed the word "initially". It was done initially. That does not mean it persists.

How is it ensured that the average ELO rating doesn't start deviating over time from 1500?

It isn't. It does start deviating over time in very obvious ways. Some deviation is built in via the "k" factor. My "k" factor is 20. If I play a "k" factor 10 player then our rating changes won't match. For that game my rating will change by twice as much as the other player's rating. Similarly when I play a "k" factor 40 player the other player's rating will change by twice as much as my rating.

Also when a Kasparov retires from FIDE rated chess before senility has reduced his rating to the average (whatever that now is) he takes his above average rating out of the system and reduces the overall average.

Looking at the averages for FIDE rated players in October (I haven't yet loaded the November data) we see that they are different for the different time controls:

Standard = 1652
Rapid = 1576
Blitz = 1647

Answer 3

How does the algorithm that is used in the chess world end up setting this absolute scale?

The algorithms used are described in article 8 of the FIDE Rating Regulations:

8. The working of the FIDE Rating System

The FIDE Rating system is a numerical system in which fractional scores are converted to rating differences and vice versa. Its function is to produce scientific measurement information of the best statistical quality.

8.1

The rating scale is an arbitrary one with a class interval set at 200 points. The tables that follow show the conversion of fractional score 'p' into rating difference 'dp'. For a zero or 1.0 score dp is necessarily indeterminate but is shown notionally as 800. The second table shows conversion of difference in rating 'D' into scoring probability 'PD' for the higher 'H' and the lower 'L' rated player respectively. Thus the two tables are effectively mirror-images.

8.1a

The table of conversion from fractional score, p, into rating differences, dp
[large table skipped. See original link if you really want to see it]

8.1b

Table of conversion of difference in rating, D, into scoring probability PD, for the higher, H, and the lower, L, rated player respectively.
[Table skipped]

8.2 Determining the Rating 'Ru' in a given event of a previously unrated player.

8.21

If an unrated player scores zero in his first event his score is disregarded. First determine the average rating of his competition 'Rc'.
(a) In a Swiss or Team tournament: this is simply the average rating of his opponents.
(b) The results of both rated and unrated players in a round-robin tournament are taken into account. For unrated players, the average rating of the competition 'Rc' is also the tournament average 'Ra' determined as follows:

(i) Determine the average rating of the rated players 'Rar'.
(ii) Determine p for each of the rated players against all their opponents.
Then determine dp for each of these players.
Then determine the average of these dp = 'dpa'.
(iii) 'n' is the number of opponents.
Ra = Rar - dpa x n/(n+1)

8.22

If he scores 50%, then Ru = Ra

8.23

If he scores more than 50%, then Ru = Ra + 20 for each half point scored over 50%

8.24

If he scores less than 50% in a Swiss or team tournament: Ru = Ra + dp

8.25

If he scores less than 50% in a round-robin: Ru = Ra + dp x n/(n+1).

8.3

The Rating Rn which is to be published for a previously unrated player is then determined as if the new player had played all his games so far in one tournament. The initial rating is calculated using the total score against all opponents. It is rounded to the nearest whole number.

8.4

If an unrated player receives a published rating before a particular tournament in which he has played is rated, then he is rated as a rated player with his current rating, but in the rating of his opponents he is counted as an unrated player.

> 8.5 Determining the rating change for a rated player

8.51

For each game played against a rated player, determine the difference in rating between the player and his opponent, D.

8.52

If the opponent is unrated, then the rating is determined at the end of the event. This applies only to round-robin tournaments. In other tournaments games against unrated opponents are not rated.

8.53

The provisional ratings of unrated players obtained from earlier tournaments are ignored.

8.54

A difference in rating of more than 400 points shall be counted for rating purposes as though it were a difference of 400 points.

8.55

(a) Use table 8.1(b) to determine the player’s score probability PD
(b) ΔR = score – PD. For each game, the score is 1, 0.5 or 0.
(c) ΣΔR x K = the Rating Change for a given tournament, or Rating period.

8.56

K is the development coefficient. K = 40 for a player new to the rating list until he has completed events with at least 30 games.
K = 20 as long as a player's rating remains under 2400.
K = 10 once a player's published rating has reached 2400 and remains at that level subsequently, even if the rating drops below 2400.
K = 40 for all players until their 18th birthday, as long as their rating remains under 2300.
If the number of games (n) for a player on any list for a rating period multiplied by K (as defined above) exceeds 700, then K shall be the largest whole number such that K x n does not exceed 700.

8.57

The Rating Change is rounded to the nearest whole number. 0.5 is rounded up (whether the change is positive or negative).

8.58

Determining the Ratings in a round-robin tournament. Where unrated players take part, their ratings are determined by a process of iteration. These new ratings are then used to determine the rating change for the rated players. Then the ΔR for each of the rated players for each game is determined using Ru(new) as if an established rating.

So, in answer to:

does it always try to make sure that the mean score is 1500, by adjusting everyone's score uniformly when the mean deviates?

As you can see from article 8.5, "No".

Or does it simply always assign a particular initial score?

As you can see from articles 8.2 - 8.4 the answer is again "No".